Biomedical Engineering Reference
In-Depth Information
The effectiveness factor can be computed by
r AS
r A ¼
k c a ð C Ab C AS Þ
r max C Ab
K A þ C Ab
k c aC Ab
r max
K A
C Ab
C AS
C Ab
h e ¼
¼
1 þ
1
"
3
5
s
1
4
2
k c aC Ab
r max
K A
C Ab
1
2
K A
r max
k c aC Ab
K A
r max
k c aC Ab
K A
C Ab
¼
1 þ
1 þ
C Ab þ
1
C Ab
þ
(17.12)
If we define the external mass transfer Thiele modulus as the ratio of the reaction rate eval-
uated at fluid phase bulk conditions to the maximum possible mass transfer rate,
r max C Ab
K A þ C Ab
f e ¼ r A ; b
r max
ðk c aÞðK A þ C Ab Þ
k c aC Ab ¼
k c aC Ab ¼
(17.13)
Eqn (17.12) is then reduced to
( 1 þ f e
2
9
=
s
1
4
2
h e ¼ f e
K A
C Ab
K A
C Ab
K A
C Ab
1 þ
1
f e ð1 þ
f e Þ
þ
;
(17.14)
"
3
s
1
¼ 1 þ f e
2
K A
C Ab
4f e
ð1 þ
K A
C Ab
5
1 þ
1
1
1 þ
f e Þ 2
f e
Fig. 17.2 shows the effectiveness factor as computed by Eqn (17.14) . The horizontal axis is
a function of the mass transfer coefficient,
U 0:5931
d 0:4069
p
k c a ð K A þ C Ab Þ
r max
f 1
e
¼
f
(17.15)
which is obtained based on the fact that r max is proportional to the surface area and the mass
transfer coefficient k c is found in Table 17.2 . Thus, Fig. 17.2 indicates that if one plots the effec-
tiveness factor (or the apparent reaction rate) against U 0:5931 =d 0:406 p , it increases initially and
finally levels off. If the apparent reaction rate is not increasing with increasing flow rate or
decreasing catalyst particle size, the external mass transfer effects are negligible.
When the flow rate is low (or low agitation) and/or catalyst particle size is large, external
mass transfer effects dominate the reaction system. When external mass transfer is limiting,
the concentration of A on the catalyst surface becomes negligible, and
r A ¼
h e ðr A ; b Þ¼k c aðC Ab C AS Þ z k c aC Ab
(17.16)
If we replot the effectiveness factor on a log-scale, Fig. 17.3 appears better at smaller mass
transfer rates.When externalmass transfer isdominant in the reaction system, the apparent reac-
tion rate is of first order, irrespective of the intrinsic kinetics. For the limiting cases, Eqn (17.14) is
reduced to
min f e ;
h e ¼
1
;
for K A ¼ 0
(17.17a)
Search WWH ::




Custom Search